Coupled-channel effects in elastic scattering and near-barrier fusion induced by weakly bound nuclei and exotic halo nuclei

The influence on fusion of coupling to the breakup process is investigated for reactions where at least one of the colliding nuclei has a sufficiently low binding energy for breakup to become an important process. Elastic scattering, excitation functions for sub- and near-barrier fusion cross sections, and breakup yields are analyzed for ${}^{6,7}\mathrm{Li}+{}^{59}\mathrm{Co}$. Continuum-discretized coupled-channels (CDCC) calculations describe well the data at and above the barrier. Elastic scattering with ${}^6\mathrm{Li}$ (as compared to ${}^7\mathrm{Li}$) indicates the significant role of breakup for weakly bound projectiles. A study of ${}^{4,6}\mathrm{He}$ induced fusion reactions with a three-body CDCC method for the ${}^6\mathrm{He}$ halo nucleus is presented. The relative importance of breakup and bound-state structure effects on total fusion is discussed.

Figure 1

Ratios of the elastic scattering cross sections to the Rutherford cross sections as a function of c.m. angle for the ${}^7\mathrm{Li}+{}^{59}\mathrm{Co}$ system [48]. The curves correspond to calculations with (solid lines) and without (dashed lines) ${}^7\mathrm{Li}$ → α$+t$ breakup couplings to the continuum for incident ${}^7\mathrm{Li}$ energies of (a) 30 MeV, (b) 26 MeV, (c) 18 MeV, and (d) 12 MeV.

Figure 2

Ratios of the elastic scattering cross sections to the Rutherford cross sections as a function of c.m. angle for the ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ system [48]. The curves correspond to calculations with (solid lines) and without (dashed lines) ${}^6\mathrm{Li}$ → α$+d$ breakup couplings to the continuum for incident ${}^6\mathrm{Li}$ energies of (a) 30 MeV, (b) 26 MeV, (c) 18 MeV, and (d) 12 MeV.

Figure 3

CDCC calculation for the angular distribution of the ${}^6\mathrm{Li}$ $\to \alpha +d$ sequential breakup via the 2.18 MeV $3^{+}$ state of ${}^6\mathrm{Li}$ compared to the data of Bochkarev et al. [60] as obtained for the ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ reaction at 41 MeV.

Figure 4

Total reaction cross sections (solid curve), integrated total BU cross sections (dot-dashed curve), integrated ${}^7\mathrm{Li}$ ground state reorientation plus $1/2^{-}$ inelastic excitation cross sections (dashed curve) and BPM fusion cross sections (dotted curve) obtained from the CDCC calculations for the ${}^7\mathrm{Li}+{}^{59}\mathrm{Co}$ system. The filled and open circles denote the total reaction cross sections obtained from the best OM fits and the measured TF cross sections [44], respectively. The filled triangles denote the summed DWBA estimates for single nucleon stripping and pickup reactions, see text for details.

Figure 5

Total reaction cross sections (solid curve), integrated total BU cross sections (dot-dashed curve), integrated ${}^6\mathrm{Li}$ 2.18 MeV $3^{+}$ sequential BU cross sections (dashed curve) and BPM fusion cross sections (dotted curve) obtained from the CDCC calculations for the ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ system. The filled and open circles denote the total reaction cross sections obtained from the best OM fits and the measured TF cross sections [44], respectively. The open square denotes the ${}^6\mathrm{Li}$ 2.18 MeV $3^{+}$ sequential BU cross section reported in [60]. The filled triangles denote the summed DWBA estimates for single nucleon stripping and pickup reactions, see text for details.

Figure 6

Energy dependence of the real and imaginary parts of the bare plus DPP potentials as generated by the CDCC calculations (filled circles) and the best OM fits potentials (open circles) for the ${}^7\mathrm{Li}+{}^{59}\mathrm{Co}$ system at a radial distance of $r=9.7$ fm as discussed in the text.

Figure 7

As for Fig. 6 but for the ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ system at a radial distance of $r=9.5$ fm.

Figure 8

Energy dependence of TF cross sections for the ${}^6\mathrm{He}+{}^{59}\mathrm{Co}$ reaction obtained with the CDCC method [29]. The dashed and thin curves correspond respectively to CDCC calculations with and without continuum couplings. The experimental TF cross sections for the ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ system [44] are given for the sake of comparison. For each reaction, the incident energy is normalized by the Coulomb barrier of the effective potential [69, 70].

Figure 9

The ${}^6\mathrm{He}+{}^{59}\mathrm{Co}$ TF excitation functions are the same as in Fig. 8 and are compared with ${}^4\mathrm{He}+{}^{59}\mathrm{Co}$ TF excitation functions. The TF cross sections of ${}^4\mathrm{He}+{}^{59}\mathrm{Co}$ were taken from [71] and standard calculations (solid curve) were performed as discussed in the text.